Geodesic
Theory of coverings in the study of Riemann surfaces
Ewa Tyszkowska1
1 Institute of Mathematics University of Gdańsk Wita Stwosza 57 80-952 Gdańsk, Poland
Colloquium Mathematicum, Tome 127 (2012) no. 2, pp. 173-184

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

For a $G$-covering $Y\rightarrow Y/G=X$ induced by a properly discontinuous action of a group $G$ on a topological space $Y$, there is a natural action of $\pi (X,x)$ on the set $F$ of points in $Y$ with nontrivial stabilizers in $G$. We study the covering of $X$ obtained from the universal covering of $X$ and the left action of $\pi (X,x)$ on $F$. We find a formula for the number of fixed points of an element $g\in G$ which is a generalization of Macbeath's formula applied to an automorphism of a Riemann surface. We give a new method for determining subgroups of a given Fuchsian group.
DOI : 10.4064/cm127-2-3
Keywords: g covering rightarrow induced properly discontinuous action group topological space there natural action set points nontrivial stabilizers study covering obtained universal covering action formula number fixed points element which generalization macbeaths formula applied automorphism riemann surface method determining subgroups given fuchsian group

Ewa Tyszkowska 1

1 Institute of Mathematics University of Gdańsk Wita Stwosza 57 80-952 Gdańsk, Poland 
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Ewa Tyszkowska. Theory of coverings in the study of
 Riemann surfaces. Colloquium Mathematicum, Tome 127 (2012) no. 2, pp. 173-184. doi: 10.4064/cm127-2-3

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